Polychromatic polynomials (Q1567655)

\textit{T. Brylawski} [J. Comb. Theory, Ser. B 30, 233-246 (1981; Zbl 0463.05031)] defined a graph invariant, called the polychromate, which provides information including the Tutte polynomial and hence the chromatic polynomial. The present authors refine the polychromate to a graph invariant incorporating a root vertex, and show that this rooted polychromate distinguishes all nonisomorphic rooted trees. They further refine to an invariant called the strong polychromate, which they conjecture uniquely identifies almost all graphs.